The Abel Prize for 2013 has been awarded to Pierre Deligne, Professor Emeritus in the School of Mathematics at the Institute for Advanced Study, Princeton, for

seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields.

A press release associated with the prize gives more background detail on his field:

Geometric objects such as lines, circles and spheres can be described by simple algebraic equations. The resulting fundamental connection between geometry and algebra led to the development of algebraic geometry, in which geometric methods are used to study solutions of polynomial equations, and, conversely, algebraic techniques are applied to analyze geometric objects. Over time, algebraic geometry has undergone several transformations and expansions, and has become a central subject with deep connections to almost every area of mathematics. Pierre Deligne played a crucial role in many of these developments.

One of the prizes vying for the moniker ‘the Nobel Prize of mathematics‘, the Abel Prize has been awarded annually since 2003 by the Norwegian Academy of Science and Letters “for outstanding scientific work in the field of mathematics”.

One of Deligne’s achievements was the proof of the Weil conjectures, which entailed the proof of the Ramanujan-Petersson conjecture about the ‘tau’ function. In the OEIS entry for the tau numbers, there is a quote from Don Zagier:

The proof of these formulae, if written out from scratch, has been estimated at 2000 pages; in his book Manin cites this as a probable record for the ratio: `length of proof:length of statement’ in the whole of mathematics.

The award citation, along with a biography and accounts of his work by Timothy Gowers and Arne B. Sletsjøe, are available on the Abel Prize 2013 webpage. Tim Gowers has posted on his blog some more links to background reading and said that a video of the talk he gave at the award ceremony on Deligne’s work will be available via the Abel Prize webpage in due course.

### More information

The Abel Committee’s citation of Pierre Deligne.

The Work of Pierre Deligne by Timothy Gowers – written version of the talk he gave at the ceremony.

A post on Gowers’s weblog with links to more background reading.

Pierre Deligne’s homepage at the IAS.

Tau numbers at the OEIS.